Question: Rewrite as a simplified fraction. ${0.90\overline{4} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 904.4444...\\ 100x &= 90.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 814}$ ${x = \dfrac{814}{900}} $ ${x = \dfrac{407}{450}} $